Question

Photographer 1 charges a $100 fee for a photo shoot plus a rate of $75 per hour. The prices charged by Photographer 2 are shown in the table below.


Photographer 2
Time (hours) Cost (dollars)
0 0
1 125
2 250
3 375

For a 5-hour photo shoot, which photographer would be less expensive? How much less expensive? Show your work.

​

Answer 1

To determine which photographer is less expensive for a 5-hour photo shoot, we can calculate the total cost for each photographer.

### Photographer 1
Photographer 1 charges:
- A base fee of $100
- An hourly rate of $75 per hour

For a 5-hour photo shoot, the total cost can be calculated as follows:

\[
\text{Total Cost} = \text{Base Fee} + (\text{Hourly Rate} \times \text{Number of Hours})
\]
\[
\text{Total Cost} = 100 + (75 \times 5)
\]
\[
\text{Total Cost} = 100 + 375
\]
\[
\text{Total Cost} = 475
\]

Thus, the total cost for Photographer 1 for a 5-hour shoot is **$475**.

### Photographer 2
Photographer 2's prices are given in the table, and we can see the costs for each hour:

- For 1 hour: \$125
- For 2 hours: \$250
- For 3 hours: \$375
- For 4 hours: The pattern indicates an increase of \$125 per hour, so for 4 hours, it would be:
\[
4 \times 125 = 500
\]
- For 5 hours: Continuing the pattern, we can find that:
\[
5 \times 125 = 625
\]

Thus, for a 5-hour photo shoot, the total cost for Photographer 2 is **$625**.

### Conclusion
Now we can compare the two costs:
- Cost of Photographer 1 for 5 hours: **$475**
- Cost of Photographer 2 for 5 hours: **$625**

To find out how much less expensive Photographer 1 is than Photographer 2:

\[
\text{Difference} = 625 - 475 = 150
\]

So, Photographer 1 is **$150** less expensive than Photographer 2 for a 5-hour photo shoot.